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Zusammenfassung:
The analytical solutions for gravitational effects of a spherical shell and a spherical zonal band are commonly used as benchmark for the superposition of discretized spherical mass bodies (e.g., tesseroid) in gravity field modeling. The error level thus obtained is usually considered to be representative of the discretization error level of single tesseroids. However, this is not the case in general. When superposing individual tesseroids forming the whole spherical shell and spherical zonal band, their individual discretization errors will partially cancel, the so-called superposition error elimination effect (SEEE). In previous studies, the SEEE of the spherical shell and spherical zonal band has not been taken seriously, and it needs to be investigated carefully.
In this contribution, we derive analytical formulas of the signal of derivatives of the gravitational potential up to third-order of a tesseroid when the computation point is situated on the polar axis. Numerical results indicate that the SEEE does not exist for the gravitational components V, Vz, Vzz, and Vzzz of a spherical zonal band discretized into tesseroids, but it can be found for the Vxx and Vyy. The superposition error effect exists for the Vxxz and Vyyz of a spherical zonal band on the overall average. In most instances, the SEEE arises from a spherical shell discretized into tesseroids.
In summary, numerical experiments demonstrate the existence of the SEEE both for a spherical zonal band and a spherical shell and show that the analytical solutions for a tesseroid can contribute to further investigations of the SEEE.
